Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
266 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10621898 | C2 | semidirect |
| 2. #13063345 | C2 | direct (N × H) |
| 3. C2×#10621885 | C2 | semidirect |
| 4. C2×#10621883 | C2 | semidirect |
| 5. C2×#10621884 | C2 | semidirect |
| 6. C2×#10621882 | C2 | semidirect |
| 7. C22×C43⋊C8 | C2 | semidirect |
| 8. C2×#41×C43 | C2 | semidirect |
| 10. #41×C43 | C22 | semidirect |
| 18. #10621898 | C22 | semidirect |
| 22. #10621885 | C22 | semidirect |
| 23. #10621884 | C22 | semidirect |
| 24. #10621883 | C22 | semidirect |
| 25. #10621882 | C22 | semidirect |
| 28. C2×C43⋊C8 | C22 | semidirect |
| 66. C2×C43 | #135 | semidirect |
| 70. C43 | C2×#135 | semidirect |
| 72. C2×#41 | D43 | semidirect |
| 82. #41 | C2×D43 | semidirect |
| 137. C2 | #13063345 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10621898 | 2 |
| #13063345 | 2 |
| C2×#10621885 | 2 |
| C2×#10621883 | 2 |
| C2×#10621884 | 2 |
| C2×#10621882 | 2 |
| C22×C43⋊C8 | 2 |
| C2×#41×C43 | 2 |
| C2×#135 | 43 |